A new degree for S1-invariant gradient mappings and applications

Abstract

We construct a new degree for S1-invariant gradient maps where the classical degree gives little information. The main technical result needed is a new result on generic homotopies. We apply this degree to obtain a global bifurcation theorem which applies to cases where classical results give limited information.We apply our results to obtain a bifurcation theorem for periodic solutions of Hamiltonian systems and for a problem in elasticity. We also obtain new results on bifurcation for elliptic equations on domains with an S1 symmetry.